Question

Consider a population proportion p = 0.68. Calculate the expected value and the standard error of with n = 20. Is it appropriate to use the normal distribution approximation for ? Calculate the expected value and the standard error of with n = 50. Is it appropriate to use the normal distribution approximation for ?

Answer 1

Answer: a) 0.68, 0.1043, b) 0.68, 0.066

Explanation:

Since we have given that

p = 0.68

n= 20

Expected value = 0.68

So, Standard error would be

`\sqrt{(p(1-p))/(n)}\\\\=\sqrt{(0.68* 0.32)/(20)}\\\\=0.1043`

if n = 50

Expected value = 0.68

So, Standard error would be

`\sqrt{(p(1-p))/(n)}\\\\=\sqrt{(0.68* 0.32)/(50)}\\\\=0.0659\approx 0.066`

In both the cases,

Yes it is appropriate to use the normal distribution for expected value and standard error.